Moments of the ruin time and the total amount of claims until ruin in a diffusion risk process

- Journal title : Journal of the Korean Data and Information Science Society
- Volume 27, Issue 1, 2016, pp.265-274
- Publisher : Korean Data and Information Science Society
- DOI : 10.7465/jkdi.2016.27.1.265

Title & Authors

Moments of the ruin time and the total amount of claims until ruin in a diffusion risk process

Kim, Jihoon; Ahn, Soohan;

Kim, Jihoon; Ahn, Soohan;

Abstract

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

Keywords

Augmented matrix;diffusion risk process;exponential claim;Poisson process;

Language

English

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